Homomorphic Encryption

What is Homomorphic Encryption? Encryption that allows computation on encrypted data without decrypting it, enabling privacy-preserving ML inference and training.

Types of Homomorphic Encryption

How it Works

[Plaintext Data] --> [Encrypt] --> [Ciphertext]
                                        |
                                        v
                              [Compute on Ciphertext]
                                        |
                                        v
                               [Encrypted Result]
                                        |
                                        v
                     [Decrypt] --> [Plaintext Result]

Key property: Decrypt(Compute(Encrypt(x))) = Compute(x)

Operations

# Conceptual example
from tenseal import BFVContext, BFVVector

# Setup
context = BFVContext.create(poly_modulus_degree=4096)

# Encrypt
encrypted_x = BFVVector.encrypt(context, [1, 2, 3])
encrypted_y = BFVVector.encrypt(context, [4, 5, 6])

# Compute on encrypted data
encrypted_sum = encrypted_x + encrypted_y
encrypted_product = encrypted_x * encrypted_y

# Decrypt
result = encrypted_sum.decrypt()  # [5, 7, 9]

HE for ML Inference

def encrypted_inference(encrypted_input, encrypted_weights):
    # Linear layer: y = Wx + b
    # Works because addition and multiplication are supported
    encrypted_output = encrypted_weights @ encrypted_input
    encrypted_output += encrypted_bias

    # Activation: approximate with polynomial
    # ReLU approximated as polynomial for HE compatibility
    encrypted_activated = polynomial_approx_relu(encrypted_output)

    return encrypted_activated

Limitations

Libraries

Use Cases

Practical Considerations

• Very computationally expensive
• Often combined with other techniques (MPC)
• Best for specific, high-value privacy scenarios
• Approximate operations needed for non-linear functions